• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.211-223
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• 2009

Transient response analysis can be conducted either in the time domain, or via the frequency domain. Sometimes a frequency domain method (FDM) has advantages over a time domain method. A practical issue in the FDM is to find out an appropriate extended period, which may be affected by several factors, such as the excitation duration, the system damping, the artificial damping, the period of interest, etc. In this report, the extended period of the FDM based on the Duhamel's integral is investigated. This Duhamel's integral based FDM does not involve the unit impulse response function (UIRF) beyond the period of interest. Due to this fact, the ever-lasting UIRF can be simply set as zero beyond the period of interest to shorten the extended period. As a result, the preferred extended period is the summation of the period of interest and the excitation duration. This conclusion is validated by numerical examples. If the extended period is too short, then the front portion of the period of interest is more prone to errors than the rear portion, but the free vibration segment is free of the wraparound error.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.210-216
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• 1996

Spectral element method(SEM) has been recognized to provide accurate structural dynamic responses even at high frequency. The Duhamel's integral based SEM developed by the authors for the structures under dynamic distributed loads does not take into account the zero frequency effect and requires significant computational time due to the integration procedure of Duhamel's integral. Hence, in this paper, a new SEM algorithm is proposed. This new algorithm is based on the FEM-type procedure for the distributed loads and includes the zero frequency correction to improve the accuracy. Some numerical results are illustrated to prove the accuracy of present new SEM algorithm.

• Bulletin of the Society of Naval Architects of Korea
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• v.14 no.3
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• pp.5-12
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• 1977

In shipyard production processes, lots of steel plates are assembled by welding. Some rectangular steel plates are buttwelded to build a large block in panel production lines. There are some advantages to take the tandem arc welding in butt joints of rectangular plates with respect to welding speed. Hence, the thermal stresses and the temperature distribution of the tandem arc welding are studied in this paper. The solutions in the case of the infinite plate with two instantaneous point heat sources have been obtained. And then the solutions have been extended to the case of two moving heat sources corresponding to the tandem arc welding with the aid of Duhamel's superposition integral. It was found that the temperature distribution was good agreement with the results of the experiments by Rosenthal and Park and the thermal stresses calculated were acceptable with respect to a physical phenomenon. These solutions are able to be applied to the problem such as a line heating.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.1
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• pp.54-60
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• 1981

This paper presents the dynamic behaviour of a simple beam subjected to moving loads and prebending moments. The velocity of the moving loads is assumed constant, and the prebending moment is assumed to be M. The fundamental equation of motion of the beam is derived from the principle of virtual works and solved by using Duhamel's Integral. In this paper we found that the dimensionless deflection at the middle of beam was related with prebending moment(M), velocity(V) and magnitude of the moving load(F) ; that is y/y$_{0}$=1/1-.betha.$^{2}$-.pi.M/Fl The faster the velocity becomes, the deeper the maximum deflection becomes. And the maximum deflection at the middle of beam was occurred after the moving load passed the midpoint of beam.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.2
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• pp.69-78
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• 1995

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine(SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the onlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increament. The method is applied to a nonlinear generic model of the high pressure oxygen turthods, the convolution approach proved to be more accurate and highly more efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance(IHB) method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic(subsynchronous) responses of the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-totor models to their coordinates at the bearing clearances.

• Bulletin of the Society of Naval Architects of Korea
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• v.13 no.1
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• pp.25-34
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• 1976

Analytical solutions for the transient temperature and quasi-static thermal stresses which arise in thin plates subjected to an instantaneous point source of heat have been investigated. And the solutions have been extended to the case of a moving source of heat with the aid of the Duhamel's superposition integral. For finite disk an experiment was conducted, the measured temperature histories show a good agreement with the theoretical temperature histories, And the histories of thermal stresses show a good qualitative agreement with the physical phenomena. And also we can find out that the maximum temperature and thermal stresses and their location can be estimated by using the solutions for infinite plates instead of the solutions for a finite plate. The solutions can be used for the problems such as a welding or line heating in a hull construction.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.1
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• pp.9-22
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• 1975

As a second step of a thermal stress analysis in a watertight bulkhead plate during welding of a spool type penetration piece, is idealized as a thin circular disk with a clamped boundary. The exact solution for the transient temperature distribution and associated quasi-static thermal stresses which arise in a circular disk subjected to an instantaneous point source of heat acting in its interior has been obtained. And the solutions have been extended to the case of moving source of heat with the aid of the Duhamel's superposition integral and the results finally derived have been compared with the other results from the typical cases. The solutions can be applied to the problem such as a welding of a penetration piece on the watertight bulkhead and also applicable to the problems which occur in cutting or welding.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.2
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• pp.13-34
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• 1975

Analytical solutions for the transient temperature distribution and quasi-static thermal stresses which arise in a thin circular disk of finite radius subjected to an instantaneous point source acting in its interior have been obtained. And the solutions have been extended to the case of a moving heat source with the aid of the Duhamel's superposition integral. The solutions given are in the form of double infinite serieses, and their numerical results have been compared with the experimental temperature histories. It can be found out that the theoretical histories of thermal stresses show a good agreement with the experimental results and the theoretical histories of thermal stresses show a good qualitative agreement with a physical phenomena. The solutions can be applied to the problems such as a flame hardening of the cylindrical machine elements and a circular patch welding or a circular cutting of the structural member.

• Bulletin of the Society of Naval Architects of Korea
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• v.12 no.1
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• pp.1-8
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• 1975

As a first step of a thermal stress analysis in a watertight bulkhead plate during welding of a spool type penetration piece, the bulkhead plate has been idealized as infinite plate with a circular hole. The exact solution for the transient temperature distribution and the associated quasi-static thermal stress which arise in a infinite plate subjected to an instantaneous point source of heat acting on the periphery of the circular hole. And the solutions have been extended to the case of a moving heat source with the aid of the Duhamel's superposition integral. The solutions can be applied to the problems such as a circular cutting or welding of a plate.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.1A
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• pp.95-104
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• 2008

Dynamic behaviors of the two-span continuous bridge which is one of prototypes on Gyoung-Bu high-speed railway are analyzed and some methods for reducing the resonance of the bridge are proposed. The bridge is modeled as a two-span continuous beam and the load is a vehicle of TGV-K (2p+18T) with length of 380.15 meter traveling on the railway bridge at some constant velocity. The equations governing the dynamic behaviors of the bridge are partial differential equations produced by using a system with distributed mass and elasticity. The analysis of the governing equations is performed by the mode superposition method which has modal coordinates solved by Duhamel's integral. Without considering the train velocity the dynamic reponses can be greatly reduced at some special lengths of bridge. It is different from the results of simple bridges researched so far. When the dynamic responses increase rapidly to make a resonance phenomenon depending on the train velocities, the several methods are proposed to deduce the resonance.